To ensure that the Chern number does not vanish, we take an approach that is close to the famous example known as the `Haldane model' developed by F. Duncan Haldane in the late 1980s [1]}. We consider the special case of a lattice with hexagonal symmetry and lattice constant \(d\)Lattice vectors \({a}_{1}=\frac{d}{2}({e}_{x}+\sqrt{3}{e}_{y})\) , and \({a}_{2}=\frac{d}{2}(-{e}_{x}+\sqrt{3}{e}_{y})\). Taking two identical resonators per unit cell, we construct a honeycomb lattice where each `a' resonator is separated by \(d/\sqrt{3}\)  from three nearest neighbour `b' resonators, as shown in Fig. REF a. Assuming only nearest neighbour coupling between the \(a\)  and \(b\)  resonators, \(\alpha _{0,0}=\alpha _{1,0}=\alpha _{0,1}=\alpha \,{\rm exp}(-{\rm i}K_y d/\sqrt{3})\)  of equal strength \(\alpha _{1,0}=\alpha _{0,1}=\alpha \) , the coupling function \(g({K})\)  reduces to

g(K)= e-iKyd/3[1+eiKa1+eiKa2]
